login
A105385
Expansion of (1-x^2)/(1-x^5).
2
1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1
OFFSET
0,1
COMMENTS
Periodic {1,0,-1,0,0}.
Binomial transform is A103311(n+1). Consecutive pair sums of A105384.
FORMULA
G.f.: (1+x)/(1 + x + x^2 + x^3 + x^4);
a(n) = sqrt(1/5 - 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(2*sqrt(5)/25 + 1/5)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.
a(n) = A092202(n+1). - R. J. Mathar, Aug 28 2008
a(n) = a(n-1) - a(n-2) - a(n-3) - a(n-4); a(0)=1, a(1)=0, a(2)=-1, a(3)=0. - Harvey P. Dale, Mar 10 2013
MATHEMATICA
CoefficientList[Series[(1-x^2)/(1-x^5), {x, 0, 100}], x] (* or *) PadRight[{}, 100, {1, 0, -1, 0, 0}] (* or *) LinearRecurrence[{-1, -1, -1, -1}, {1, 0, -1, 0}, 100] (* Harvey P. Dale, Mar 10 2013 *)
CROSSREFS
Cf. A092202 (essentially the same).
Cf. A198517 (absolute values).
Sequence in context: A127831 A164364 A198517 * A190227 A090626 A129569
KEYWORD
sign,easy
AUTHOR
Paul Barry, Apr 02 2005
STATUS
approved